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The differential equation of the curve for which the point of tangency (closer to the x -axis) divides the segment of the tangent between the coordinate axes in the ratio 1 : 2 , is

Options

  1. Ax d y = 2 y d x
  2. Bx d y = y d x
  3. Cx d y + 2 y d x = 0
  4. Dx d y + y d x = 0

Correct answer

C. x d y + 2 y d x = 0

Step-by-step solution

Equation of the tangent is Y - y = m X - x ⇒ A ≡ x - y m , 0 , B ≡ 0 , y - m x Using section formula, we get, y = 1 ⋅ y - m x + 2 0 1 + 2 or 3 y = y - m x ⇒ m = d y d x = - 2 y x i.e. x d y + 2 y d x = 0

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